Towards Quantum Simulation of Black Holes in a dc-SQUID Array

We propose quantum simulations of 1 + 1D radial sections of different black hole spacetimes (Schwarzschild, Reissner–Nordstrøm, Kerr and Kerr–Newman), by means of a dc-SQUID array embedded on an open transmission line. This was achieved by reproducing the spatiotemporal dependence of 1 + 1D sections of the spacetime metric with the propagation speed of the electromagnetic field in the simulator, which can be modulated by an external magnetic flux. We show that the generation of event horizons—and therefore Hawking radiation—in the simulator could be achieved for non-rotating black holes, although we discuss limitations related to fluctuations of the quantum phase. In the case of rotating black holes, it seems that the simulation of ergospheres is beyond reach.

Scalarons mimicking dark matter in the Hu–Sawicki model of f(R ) gravity

In this paper, we conduct a study on the scalar field obtained from [Formula: see text] gravity via Weyl transformation of the spacetime metric [Formula: see text] from the Jordan frame to the Einstein frame. The scalar field is obtained as a result of the modification in the geometrical part of Einstein’s field equation of General Relativity. For the Hu–Sawicki model of [Formula: see text] gravity, we find the effective potential of the scalar field and calculate its mass. Our study shows that the scalar field (also named as scalaron) obtained from this model has the chameleonic property, i.e. the scalaron becomes light in the low-density region, while it becomes heavy in the high-density region of matter. Then it is found that the scalaron can be regarded as a dark matter (DM) candidate since the scalaron mass is found to be quite close to the mass of ultralight axions, a prime DM candidate. Thus, the scalaron in the Hu–Sawicki model of [Formula: see text] gravity behaves as DM. Further, a study on the evolution of the scalaron mass with the redshift is also carried out, which depicts that scalaron becomes light with expansion of the Universe and with different rates at different stages of the Universe.

The 3+1 formalism in teleparallel and symmetric teleparallel gravity

Teleparallel and symmetric teleparallel gravity offer platforms in which gravity can be formulated in interesting geometric approaches, respectively given by torsion and nonmetricity. In this vein, general relativity can be expressed in three dynamically equivalent ways which may offer insights into the different properties of these decompositions such as their Hamiltonian structure, the efficiency of numerical analyses, as well as the classification of gravitational field degrees of freedom. In this work, we take a $$3+1$$ 3 + 1 decomposition of the teleparallel equivalent of general relativity and the symmetric teleparallel equivalent of general relativity which are both dynamically equivalent to curvature based general relativity. By splitting the spacetime metric and corresponding tetrad into their spatial and temporal parts as well as through finding the Gauss-like equations, it is possible to set up a general foundation for the different formulations of gravity. Based on these results, general 3-tetrad and 3-metric evolution equations are derived. Finally through the choice of the two respective connections, the metric $$3+1$$ 3 + 1 formulation for general relativity is recovered as well as the tetrad $$3+1$$ 3 + 1 formulation of the teleparallel equivalent of general relativity and the metric $$3+1$$ 3 + 1 formulation of symmetric teleparallel equivalent of general relativity. The approach is capable, in principle, of resolving common features of the various formulations of general relativity at a fundamental level and pointing out characteristics that extensions and alternatives to the various formulations can present.

Classical solutions and their double copy in split signature

The three-point amplitude is the key building block in the on-shell approach to scattering amplitudes. We show that the classical objects computed by massive three-point amplitudes in gauge theory and gravity are Newman-Penrose scalars in a split-signature spacetime, where three-point amplitudes can be defined for real kinematics. In fact, the quantum state set up by the particle is a coherent state fully determined by the three-point amplitude due to an eikonal-type exponentiation. Having identified this simplest classical solution from the perspective of scattering amplitudes, we explore the double copy of the Newman-Penrose scalars induced by the traditional double copy of amplitudes, and find that it coincides with the Weyl version of the classical double copy. We also exploit the Kerr-Schild version of the classical double copy to determine the exact spacetime metric in the gravitational case. Finally, we discuss the direct implication of these results for Lorentzian signature via analytic continuation.

Chiral asymmetries in near-horizon region of charged black hole and teleparallelism

The issue of encoding physical information into metric structure of physical theories has been discussed recently by the author in the case of black hole teleparallelism. In this paper, one obtains a teleparallel chiral currents from quantum anomalies and topological torsional invariants of Nieh-Yan type. The Pontryagin index is also obtained in the case of rotating Kerr spacetime metric of non-static black holes. Magnetic monopoles which appears in this approach can be eliminated by a torsion constraint. These ideas are applied to Kerr and Kerr–Newmann charged black holes.

Dynamical C*-algebras and Kinetic Perturbations

The framework of dynamical C*-algebras for scalar fields in Minkowski space, based on local scattering operators, is extended to theories with locally perturbed kinetic terms. These terms encode information about the underlying spacetime metric, so the causality relations between the scattering operators have to be adjusted accordingly. It is shown that the extended algebra describes scalar quantum fields, propagating in locally deformed Minkowski spaces. Concrete representations of the abstract scattering operators, inducing this motion, are known to exist on Fock space. The proof that these representers also satisfy the generalized causality relations requires, however, novel arguments of a cohomological nature. They imply that Fock space representations of the extended dynamical C*-algebra exist, involving linear as well as kinetic and pointlike quadratic perturbations of the field.

Schwarzschild Like Solution with Global Monopole in Bumblebee Gravity

In this paper, by considering Einstein-Hilbert-Bumblebee (EHB) gravity around global monopole field, we derive exactly a black hole spacetime metric. To test the effect of global monopole field and bumblebee field, which causes the spontaneous Lorentz symmetry breaking, we calculate the weak deflection angle using the Gauss-Bonnet theorem.

Equiaffine Braneworld

Higher dimensional theories, wherein our four dimensional universe is immersed into a bulk ambient, have received much attention recently, and the directions of investigation had, as far as we can discern, all followed the ordinary Euclidean hypersurface theory’s isometric immersion recipe, with the spacetime metric being induced by an ambient parent. We note, in this paper, that the indefinite signature of the Lorentzian metric perhaps hints at the lesser known equiaffine hypersurface theory as being a possibly more natural, i.e., less customized beyond minimal mathematical formalism, description of our universe’s extrinsic geometry. In this alternative, the ambient is deprived of a metric, and the spacetime metric becomes conformal to the second fundamental form of the ordinary theory, therefore is automatically indefinite for hyperbolic shapes. Herein, we advocate investigations in this direction by identifying some potential physical benefits to enlisting the help of equiaffine differential geometry. In particular, we show that a geometric origin for dark energy can be proposed within this framework.